Here, a street is a designated bike route. (You can't see it very well, but the sign says “BIKE ROUTE” with an arrow pointing upwards.)

Note: in most countries a sign denoting that a stretch of road is part of a bicycle route would not make that piece of road "designated" for bicycle use. For tagging of bicycle routes see bicycle route tagging

3m wide gravel path. Local knowledge [1] indicates that this is a shared-use path (“It is open to bicyclists, hikers, joggers and horseback riders in the spring, summer and fall and to snowmobilers, skiers and dog sledders during the winter...No ATV’s are allowed on the trail.”)

An urban path on which motorized vehicle access is forbidden. As above but no guarantees on passability. Likely without restrictions on horses. Access on foot and on a bicycle is known to be legal and possible.

(In fact, the white background notice explains that law forbids horses on special leisure walking/excercise routes - that aren't signposted - which makes this "mainly for cyclists and pedestrians" and not an agricultural track.)